We begin by looking at an estimation activity in which students use a variety of representations to estimate the number of blocks in a basket and later to help determine the actual block count.

The activity begins with the teacher giving the students several boxes of blocks and telling them how many blocks are in each box, which students may use as a reference point:

Next, the students are given the following collection of blocks and are asked to estimate the total number, without removing any blocks or counting them one by one:

Let's take a look at how one group of students approached this problem.

Richard: I think there are 50 blocks.

Barbara: I think there are more than that. (begins pointing to the blocks and counting them one by one)

Jose: We aren't supposed to count them. I don't know how many blocks there are. This is too hard.

Vanessa: I think there are 100.

Barbara: I'm still not sure what we are supposed to do - I don't understand why we can't just count them.

Richard: I think we are supposed to guess how many there are without counting them. What if we look at the boxes of blocks in the front of the room again? Maybe that will help us make a better estimate.

The group takes the container of blocks and places it next to the containers in the front of the room.

After comparing the sets of blocks, the conversation continues:

Vanessa: There are a lot more than 24.

Richard: There are even more than 45 -- so I think there are more than 50.

Barbara: I think there are a lot more than 45. I think there are 100.

Vanessa: Me too!

Jose: One hundred sounds about right.

The students report their estimates to the teacher and explain how they compared their blocks with the samples in the front of the room.